The information in an individual finite object (like a binary string) is commonly measured by its Kolmogorov complexity. One can divide that information into two parts: the information accounting for the useful regularity present in the object and the information accounting for the remaining accidental information. There can be several ways (model classes) in which the regularity is expressed. ...

abstract consistent decreasing and increasing of temperature in the short-term period that is called freezing and thaw cycles is one of the important factors of damage to crop productions. in this research as to determine freezing and thaw cycles in the khorasan razavi province, the data of daily minimum and maximum temperatures of 9 synoptic stations was used over 20 statistic years (1989-2008...

A theory of overparameterized structural models is presented. In such a model some "redundant" parameters are involved; the parameter vector is not identified, and the information matrix is not nonsingular. The minimum discrepancy function (MDF) test statistic is shown to have an asymptotic chi-squared distribution almost everywhere for a wide class of discrepancy functions. Asymptotic distribu...

In this paper we consider inference based on very general divergence measures, under assumptions of multinomial sampling and loglinear models. We define the minimum φ-divergence estimator, which is seen to be a generalization of the maximum likelihood estimator. This estimator is then used in a φ-divergence goodness-of-fit statistic, which is the basis of two new statistics for solving the prob...

Linear algebra is used to demonstrate two important assertions in the main text: (1) that the expectation value of the chi-square statistic χ is equal to the degrees of freedom—the number of data points less the number of fit parameters and (2) the “∆χ = 1” rule—which states that if any fit parameter is offset one standard deviation from its best-fit value, the minimum χ (with that parameter fi...

Various chi-square statistics are used for testing structural equation models. A commonly used chi-square is the Satorra-Bentler (SB) statistic. This is a normal-theory chi-square corrected for non-normality in the observed variables. The relationship between the SB statistic and kurtosis is developed and it is shown that the SB statistic tends to decrease with increasing kurtosis if the model ...

in some quality control applications, the quality of a process or a product is described by the relationship between a response variable and one or more explanatory variables, called a profile. moreover, in most practical applications, the qualitative characteristic of a product/service is vague, uncertain and linguistic and cannot be precisely stated. the purpose of this paper is to propose a ...